Jasmien Brown hfyf7ug

Question

Provide an appropriate response. Use the Standard Normal Table to find the probability.

The distribution of cholesterol levels in teenage boys is approximately normal

with μ=170

and

σ=30

​(Source: U.S. National Center for Health​ Statistics). Levels above 200 warrant attention. Find the probability that a teenage boy has a cholesterol level greater than 225.

Answer 1

We need to standardize the value first using the following formula: To determine the likelihood that a teenage boy has a cholesterol level higher than 225, we must first:

z = (x - μ) / σ

where x represents the level of cholesterol, the mean cholesterol level, and the standard deviation of cholesterol levels.

Inputting the values provided yields:

z = (225 - 170) / 30\sz = 1.83

Next, we need to determine the chance that a teenage guy has a cholesterol level higher than 225, which is represented by the area under the standard normal curve to the right of z = 1.83. The Standard Normal Table can be used to calculate this probability.

The area to the left of the z-score is given by the table, thus to get the area to the right of z = 1.83, we must subtract the area to the left of z = 1.83 from 1. The table reveals the following:

P(Z < 1.83) = 0.9664

Thus the region to the right of z = 1.83 is as follows:

P(Z > 1.83) = 1 - P(Z < 1.83) = 1 - 0.9664 = 0.0336

As a result, there is a 0.0336 or 3.36% chance that a teenage boy has cholesterol levels above 225.